It depends on your choice of strategy. There's enough of a spread of ships in the League to fight a lot of different ways, but try to do too many things at once with ships that don't support each other and the Dilgar will break you apart.
It's always a shock re- reading the Bimith's stats and realising it actually has the same speed and agility as a Hyperion; it just doesn't feel that way. The Lakara really is a brick, and tough though it is, it's probably not as tough as what the Dilgar would be able to concentrate on it.
With the Abbai, you're trapped into a slow speed, close quarters slugging match; as a Dilgar speed freak myself, the thought of concentrating against one end of the line and roll them up in detail- joy.
I'd go for the Milani and the Tiraca from the Abbai fleet as being useful in combined ops; the Tiraca to do light hunter- killer work against the Dilgar scouts, the Milani for it's lasers.
The Dilgar have great antiship in the Thorun, but real difficulties in fighter vs. fighter. Screening is possibly the only thing in the universe the Kotha might actually be good for.
The Drazi have more options than it seems from the fleet list. Between Darkhawk long range missile ship, perfect to have as support for the Kaliva, probably the second most independently combat capable carrier in the game in the Nightfalcon, high speed swarms of Sunhawks and Warbirds, and Solarhawk assassins, they can do a lot; just don't attempt to do it all at once.
For a mix- it- up fleet, Sunhawks and Warbirds. Otherwise, use the specialists to support another force, probably the Brakiri.
The Vree are always a bit on the worrying side. The Vree line warships I've found of use in a very narrow range of circumstances- the only one of which seems likely is as rearguard to a Drazi attack line. Having a few SM- and- turret Vree follow a Drazi wave in and cover them while they turn round for another pass might work, but you could go through a lot of Vree that way. The Vaarl probably is the League's best scout, and I have a lot of time for the Xixx torp saucer.
the backbone of the fleet is likely to be the Brakiri, though. Ignore the War ships. They're fire magnets. Smaller, cheaper craft can do the Brokados' job, but the Kaliva's sniping ability is too valuable to lose. Halik- Haltona pairs work well, and Super AP Precise on the Ikorta and Brikorta is always helpful.
So, basically, three strategies; standoff bombard, close assault mosh, and carrier wings.
Kaliva, Darkhawk and Xixx for long range, Brikorta, Milani, Nightfalcon for carrier ops, Sunhawk, Warbird, Halik, Haltona, Bimith for close quarters.